On the two-dimensional quantum confined Stark effect in strong electric fields

TL;DR

This paper analyzes the two-dimensional quantum confined Stark effect under strong electric fields, deriving an asymptotic expansion of eigenvalues that relates excitation frequencies to boundary curvature.

Contribution

It provides a novel asymptotic expansion of low-lying eigenvalues for the Stark Hamiltonian in strong fields, linking eigenvalues to boundary curvature under convexity conditions.

Findings

Eigenvalues follow a three-term asymptotic expansion.

Excitation frequencies are proportional to the square root of boundary curvature.

Results depend on local convexity conditions of the domain.

Abstract

We consider a Stark Hamiltonian on a two-dimensional bounded domain with Dirichlet boundary conditions. In the strong electric field limit we derive, under certain local convexity conditions, a three-term asymptotic expansion of the low-lying eigenvalues. This shows that the excitation frequencies are proportional to the square root of the boundary curvature at a certain point determined by the direction of the electric field.